Markus Quandt writes:
>when discussing linear regression assumptions with a colleague, we
>noticed that we were unable to explain WHY heteroscedasticity has
>the well known ill effects on the estimators' properties. I know
>WHAT the consequences are (loss of efficiency, tendency to
>underestimate the standard errors) and I also know why these
>consequences are undesirable. What I'm lacking is a substantial
>understanding of HOW the presence of inhomogeneous error variances
>increases the variability of the coefficients, and HOW the
>estimation of the standard errors fails to reflect this.
I'm not sure this will help, but as a general rule, if there is information
in the model that you fail to take advantage of, you will lose efficiency.
An analogy might be the loss of efficiency when you use a nonparametric test
instead of a parametric test, assuming that the parametric assumptions are
met.
A good technical reference worth consulting is Carroll and Rupert's book.
I hope this helps.
Carroll R.J. and Ruppert D. (1988) Transformation and Weighting in
Regression. New York, NY: Chapman and Hall. (ISBN: 0-412-01421-1). For the
advanced student. A rather technical book, but my favorite guide to the
difficult problem of what you should do when the variances in a regression
model are not all the same.
Steve Simon, [EMAIL PROTECTED], Standard Disclaimer.
STATS - Steve's Attempt to Teach Statistics: http://www.cmh.edu/stats
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